Isn't hard to find small punctures with the tube still stuck around the wheel?
Partially inflate the tube after the tire is pulled aside, then run a mixture of soapy water over the tube. Sure, the tire is a bit in the way, but that is still less hassle than removing the wheel. The only real danger is that the tube needs to be treated carefully to keep it from snagging on things and causing more damage.
Indeed. The only time you remove the wheel is to replace the tires.